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For how many ordered pairs (A,B) where A and B are positive integers is $AAA_7+BBB_7+111_7=666_7?$

 Apr 25, 2022
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Because they are on the same bases, we can disregard them. 

 

Now, we have the equation: \(AAA + BBB + 111 = 666\)

 

This means \(A + B = 5\)

 

The only possible cases are \((1,4)\), \((2,3)\)\((3,2)\), and \((4,1)\). Thus, are only \(\color{brown}\boxed{4}\) cases that 

 Apr 26, 2022

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